the valve on rear of rocker cover is a pcv breather it has a tiny spring in it and a rubber valve that preload on the spring is set to work with the high and lower pressures from inlet manifold to open and close, when these fail it can make car run badly idle jumps around and also can effect the fueling trim in the process as it lets in unmetered air flow in to the inlet manifold that has already been counted by the maf ie at wrong time etc,
the n14 turbo engines are prone the most to top guide moving or snapping off just because the way they are made, and are the most common to snap off the top guide as well when chain rattle, i would say the broken bits of rib are down to either a past top gude failure or you just caught yours in time,, what i would now do for piece of mind is drop sump and check in bottom and oil pick up filter for the bits of plastic, if cant find them then chances are its had a top guide failure before you owned it,, i have seen them on hard driven cars fail 24k they have seen them 80-100k rattling light hell but still no broken,
as for the mini badge i believe they are bonded on with stuff like tiger seal, if at some point you come to sell the car someone might see no badge and effect a sale from past experience
what i see in your pics is all in very good condition